Is this proof correct?

[Baron]

Prove m^[log_m (x)] = x

m^[log_m (x)] = x
log_m [m^log_m (x)] = log_m x ------> Take both sides to the log_m
(log_m x) [log_m (m)] = log_m x ------> Power law
(log_m x)*1 = log_m x ------> [log_m (m)] = 1
log_m x = log_m x

 

[Denis]

Easier (I think) to use: if a^p = b then p = log(b) / log(a)

So start with: [log_m (x)] = log(x) / log(m)